Algebra Examples

$3 (3 x + 2) {(2 x - 5)}^{- \frac{1}{4}} + 6 {(2 x - 5)}^{\frac{3}{4}}$

Step 1

Factor $3$ out of $3 (3 x + 2) {(2 x - 5)}^{- \frac{1}{4}} + 6 {(2 x - 5)}^{\frac{3}{4}}$ .

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Step 1.1

Factor $3$ out of $3 (3 x + 2) {(2 x - 5)}^{- \frac{1}{4}}$ .

$3 ((3 x + 2) {(2 x - 5)}^{- \frac{1}{4}}) + 6 {(2 x - 5)}^{\frac{3}{4}}$

Step 1.2

Factor $3$ out of $6 {(2 x - 5)}^{\frac{3}{4}}$ .

$3 ((3 x + 2) {(2 x - 5)}^{- \frac{1}{4}}) + 3 (2 {(2 x - 5)}^{\frac{3}{4}})$

Step 1.3

Factor $3$ out of $3 ((3 x + 2) {(2 x - 5)}^{- \frac{1}{4}}) + 3 (2 {(2 x - 5)}^{\frac{3}{4}})$ .

$3 ((3 x + 2) {(2 x - 5)}^{- \frac{1}{4}} + 2 {(2 x - 5)}^{\frac{3}{4}})$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 ((3 x + 2) \frac{1}{{(2 x - 5)}^{\frac{1}{4}}} + 2 {(2 x - 5)}^{\frac{3}{4}})$

Step 3

Multiply $3 x + 2$ by $\frac{1}{{(2 x - 5)}^{\frac{1}{4}}}$ .

$3 (\frac{3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}} + 2 {(2 x - 5)}^{\frac{3}{4}})$

Step 4

To write $2 {(2 x - 5)}^{\frac{3}{4}}$ as a fraction with a common denominator, multiply by $\frac{{(2 x - 5)}^{\frac{1}{4}}}{{(2 x - 5)}^{\frac{1}{4}}}$ .

$3 (\frac{3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}} + \frac{2 {(2 x - 5)}^{\frac{3}{4}} {(2 x - 5)}^{\frac{1}{4}}}{{(2 x - 5)}^{\frac{1}{4}}})$

Step 5

Combine the numerators over the common denominator.

$3 \frac{3 x + 2 + 2 {(2 x - 5)}^{\frac{3}{4}} {(2 x - 5)}^{\frac{1}{4}}}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 6

Reorder terms.

$3 \frac{2 {(2 x - 5)}^{\frac{3}{4}} {(2 x - 5)}^{\frac{1}{4}} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7

Rewrite $\frac{2 {(2 x - 5)}^{\frac{3}{4}} {(2 x - 5)}^{\frac{1}{4}} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$ in a factored form.

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Step 7.1

Multiply ${(2 x - 5)}^{\frac{3}{4}}$ by ${(2 x - 5)}^{\frac{1}{4}}$ by adding the exponents.

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Step 7.1.1

Move ${(2 x - 5)}^{\frac{1}{4}}$ .

$3 \frac{2 ({(2 x - 5)}^{\frac{1}{4}} {(2 x - 5)}^{\frac{3}{4}}) + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \frac{2 {(2 x - 5)}^{\frac{1}{4} + \frac{3}{4}} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.1.3

Combine the numerators over the common denominator.

$3 \frac{2 {(2 x - 5)}^{\frac{1 + 3}{4}} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.1.4

Add $1$ and $3$ .

$3 \frac{2 {(2 x - 5)}^{\frac{4}{4}} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.1.5

Divide $4$ by $4$ .

$3 \frac{2 {(2 x - 5)}^{1} + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.2

Simplify $2 {(2 x - 5)}^{1}$ .

$3 \frac{2 (2 x - 5) + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.3

Apply the distributive property.

$3 \frac{2 (2 x) + 2 \cdot - 5 + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.4

Multiply $2$ by $2$ .

$3 \frac{4 x + 2 \cdot - 5 + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.5

Multiply $2$ by $- 5$ .

$3 \frac{4 x - 10 + 3 x + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.6

Add $4 x$ and $3 x$ .

$3 \frac{7 x - 10 + 2}{{(2 x - 5)}^{\frac{1}{4}}}$

Step 7.7

Add $- 10$ and $2$ .

$3 \frac{7 x - 8}{{(2 x - 5)}^{\frac{1}{4}}}$